We describe an apparatus that can visualize the creation of rainbows using a cylinder of acrylic glass. The apparatus allows one to observe rainbows up to the sixth order. A brief theoretical introduction and a method to quantitatively analyze the observation are discussed. A simple lighting system is described and its divergence is computed. The effect of light divergence on rainbow formation is analyzed.

Topics
Measuring instruments, Internet, Atmospheric optical phenomena, Geometrical optics, Lenses, Optical aberrations, Transition metals, Educational aids, Educational assessment, Public policy and governance
1.
We recall two experiments of this kind:
 
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2.
Our method can be considered as an evolution of that given by
 
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3.
An introductory, geometrical approach to the rainbow may be found in
 
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4.
A very good paper on the rainbow is
 
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8.

From the point of view of Descartes, θ0 was the maximum deviation because, if compared to our mode, he measured the angle of deviation of the rays from the other side, that is, the complement to 360°.

9.
Newton’s letter to Oldenburg, secretary of the Royal Society, containing his new theory about light and colors, published in the Philos. Trans. 80, 3075–3087 (February 19, 1672). Available online at <http://rstl.royalsocietypublishing.org/content/6/69-80/3075.full.pdf>. The complete Newton’s theory of the rainbow is in his Opticks, 4th ed. (William Innis, London,
1730
), first book, Part II, Prop. IX, Prob. IV, pp. 147–156, freely available online at <http://books.google.com>.
10.

Alexander of Afrodisia, a philosopher lived between the and the 3rd century BC

11.

See Ref. 4, pp. 424–425 and Ref. 17, pp. 246–251.

12.

This is true for the natural rainbows and for ours experiment in the range of interest. Other specific situation with different refraction index or higher orders must be appropriately calculated.

13.
See Ref. 6, pp.178–179 and
 
David K.
 
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15.
J. D.
 
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 observed the vanishing of the color for drops under 300 μm of diameter, see Ref. 4, p. 432.
16.
For a popular review on the rainbow theory see
 
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17.
For a complete review of the rainbow’s theory see
 
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18.

With “acrylic glass,” we mean polymethyl methacrylate (PMMA).

19.
Divergence of solar ray is equal to apparent diameter of the sun that vary with the earth–sun distance between aphelion and perihelion. For our purpose, we considered the apparent diameter of the sun at the mean distance, that is, about 32’. See
 
Encyclopedia of the Solar System
(
Academic Press
,
San Diego, CA
,
2007
).
20.
We have found accurate refractive index data of PMMA at <http://refractiveindex.info/?group=PLASTICS&material=PMMA>.
21.
See the <http://www.gimp.org> web site.
22.

On photos 4752 × 3168 displayed at 1:1 zoom, the position of the electronic ruler can be set with a such accuracy.

23.

An exception is the 6th order that we were able to observe with sufficient intensity to perform a measure only in two photo.

24.
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McDonald
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© 2012 American Association of Physics Teachers.
2012
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